The largest county in the state of Texas is 6064 square miles larger than the smallest county in the same state. The size of the

Question

3 years ago

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largest county is 48 times the size of the smallest county plus one square mile. How large is the smallest county in the state of Texas ?

1 answer:

Ann [662] · Answer 1 · 2022-01-22T21:06:04+03:00

The smallest county is 129 square miles large.

Step-by-step explanation:

Let,

Smallest county = x

Largest county = y

According to given statement;

The largest county in the state of Texas is 6064 square miles larger than the smallest county in the same state.

y = x+6064 Eqn 1

The size of the largest county is 48 times the size of the smallest county plus one square mile.

y = 48x+1 Eqn 2

As Eqn 1 and Eqn 2 are both equal to y, therefore,

Eqn 1 = Eqn 2

$x+6064=48x+1\\6064-1=48x-x\\6063=47x\\47x=6063$

Dividing both sides by 47

$\frac{47x}{47}=\frac{6063}{47}\\x=129\ square \ miles$

The smallest county is 129 square miles large.

Keywords: linear equation, substitution method

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